To calculate the Lowest Common Multiple of polynomials, you must find the factors of each polynomial and multiply the least occurred term. Check the steps to solve the L.C.M of polynomials and example questions in the further sections of this page.

Steps to Calculate L.C.M of Polynomials

Follow the detailed procedure to get the lowest common factor of polynomials mentioned below. These guidelines make it easy for you during the calculations.

• Get the factors of each polynomial.
• Identify common factors.
• Multiply the common factors and extra factors.

Some Examples on the Lowest Common Multiple of Polynomials

Example 1:

Find the lowest common multiple of x² − x, x², (x − 1)².

Solution:

Factorizing x² − x by taking the common factor ‘x’ we get,

= x(x − 1)

Also, factorizing x² we get

= x * x

Also, factorizing (x − 1)² we get,

= (x – 1) * (x – 1)

Therefore, the L.C.M. of x² − x, x², (x − 1)² is x²(x – 1)².

Example 2:

Find the L.C.M of n² − 3n + 2, n² − 4.

Solution:

Factorizing n² − 3n + 2 by splitting the middle term.

= n² – 2n – n + 2

= n (n – 2) -1 (n – 2)

= (n – 1) (n – 2)

Factorizing n² − 4 by using a² – b² formula.

= n² – 2²

= (n – 2) (n + 2)

Therefore, the L.C.M. of n² − 3n + 2, n² − 4 is (n – 2) (n + 2) (n – 1).

Example 3:

Find the least common multiple of 8x − 4, 6x² + x − 2.

Solution:

Factorizing 8x – 4 by taking common ‘4’.

= 4(2x – 1)

Factorizing 6x² + x – 2 by splitting the middle term.

= 6x² + 4x – 3x – 2

= 2x(3x + 2) – 1(3x + 2)

= (3x + 2) (2x – 1)

Therefore, the L.C.M of 8x − 4, 6x² + x − 2 is 4(2x-1) (3x+2).

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